Pythagoras Theroem — Formula Sheet

BC^2 = AB^2 + AC^2

AB^2 = AC^2 + BC^2 ⇒ ∠ACB = 90°

AB^2 = BC^2 + AC^2 ⇒ ΔABC is right-angled with ∠C = 90°

AB^2 > BC^2 + AC^2 ⇒ ΔABC is obtuse-angled with ∠C > 90°

AB^2 < BC^2 + AC^2 ⇒ ΔABC is acute-angled with ∠C < 90°

In triangle ABC with angle ABC = 90 degrees, side AC is the hypotenuse.

Example 2

In triangle XYZ right-angled at Z, XY = 15 cm and XZ = 9 cm, so YZ = 12 cm.

Example 3

In triangle PQR right-angled at R, PQ = 25 cm and QR = 20 cm, so PR = 15 cm.

A triangle with sides 20 cm, 9 cm, and 12 cm is not right-angled because 20^2 = 400 and 9^2 + 12^2 = 225, and these are not equal.